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Unit 1: Foundations of Multiplication & Division
DRAFT
CCSSM Units of Study are identified in the Standards Maps for each grade. Resources in a math unit are differentiated to meet the
needs of teachers in planning instruction:
• For teachers desiring a higher level of support, a series of lessons are identified to provide a beginning foundation. Additional
resources that can be implemented based on assessment data.
• For teachers who desire to plan their own series of lessons, targeted resources for instruction and assessment are identified.
Regardless of which option is selected, it is understood that teachers must customize instruction to meet the needs of
students in their classrooms using ongoing, balanced assessment.
Prior experiences:
Unit Rationale: CCSSM Progressions
Future experiences:
- Determining even numbers of
members in groups
- Work with arrays up to 5x5 as an
addition strategy
- Write equations to represent
arrays
- Partition rectangles into rows,
columns emphasizing samesized squares
- Mentally adding 10, 100 to any
given number (100-900)
Current Learning Experiences:
- Apply understanding of
multiplication models, place
value, properties of operations
- Develop, discuss, and use
efficient, accurate,
generalizable methods
- Use estimation and mental
strategies as tools for checking
reasonableness of solutions
- Mentally calculate quotients
- Interpret remainders
•
•
•
•
•
•
•
Develop understanding of multiplication, division
through activities and problem-solving
Focus on equal-sized groups, arrays, area models
Understand multiplication as unknown product
Understand division as unknown factor problem
Use properties of operations (not formalized yet)
Comparing a variety of strategies
Learning the relationship between multiplication
and division
OA Learning Progressions
Essential Questions:
What are ways to represent multiplication and division so I can better understand these operations?
How are multiplication and division related?
What strategies can I learn to help me understand these operations and their solutions?
STANDARDS: Content and Practices
Big Ideas, Targets, Language
DECONSTRUCTED CONTENT (for this unit only)
Represent and solve problems involving
multiplication and division.
3.OA.1 Interpret products of whole numbers, e.g., interpret 5 ×
7 as the total number of objects in 5 groups of 7 objects
each. For example, describe a context in which a total
number of objects can be expressed as 5 × 7.
3.OA.2 Interpret whole-number quotients of whole numbers,
e.g., interpret 56 ÷ 8 as the number of objects in each share
when 56 objects are partitioned equally into 8 shares, or as
a number of shares when 56 objects are partitioned into
equal shares of 8 objects each. For example, describe a
context in which a number of shares or a number of groups
can be expressed as 56 ÷ 8.
3.OA.3 Use multiplication and division within 100 to solve word
problems in situations involving equal groups, arrays, and
measurement quantities, e.g., by using drawings and
equations with a symbol for the unknown number to
represent the problem.
3.OA.4 Determine the unknown whole number in a
multiplication or division equation relating three whole
numbers. For example, determine the unknown number that
makes the equation true in each of the equations 8 × ? = 48,
5 = � ÷ 3, 6 × 6 = ?.
Curriculum, Instruction, & Assessment
Multiplication and division both involve a total amount, a specified
number of groups, and an amount in each group.
Multiplication and division problems can have an unknown in any
position (group, number in each group, total amount)
Multiplication and division are inverse operations and there are
related facts (“fact families”) for both.
Fluency is based on strategies that make sense to students and
that help build visual images for the brain to connect to and build
upon.
Student-friendly Learning Target Eng Sp “I can…”
Language Functions to emphasize in unit:
Defining, Asking Informational Questions (MP 4)
Describing, Predicting (MP 7)
Unit Vocabulary
Area
Array
Estimate
Factor
Inverse operation
Multiple
Equal
Odd, Even numbers
Grade 3 Vocabulary Cards ENG SP List
K-5 Vocab Activities
SBAC Glossary
Maths Dictionary
and Charts
Multi-Language Dictionary
Virtual Library of Math Literature
Rev. May 3, 2013
Salem-Keizer Public Schools
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Unit 1: Foundations of Multiplication & Division
DRAFT
Understand properties of multiplication and the relationship between multiplication and division
3.OA.5 Apply properties of operations as strategies to multiply and divide. (Students need not use formal terms for these properties.)
Examples: If 6 × 4 = 24 is known, then 4 × 6 = 24 is also known. (Commutative property of multiplication.)
3 × 5 × 2 can be
found by 3 × 5 = 15, then 15 × 2 = 30, or by 5 × 2 = 10, then 3 × 10 = 30. (Associative property of multiplication.) Knowing that 8 ×
5 = 40 and 8 × 2 = 16, one can find 8 × 7 as 8 × (5 + 2) = (8 × 5) + (8 × 2) = 40 + 16 = 56. (Distributive property.)
3.OA.6 Understand division as an unknown-factor problem. For example, find 32 ÷ 8 by finding the number that makes 32 when
multiplied by 8.
Multiply and divide within 100.
3.OA.7 Fluently multiply and divide within 100, using strategies such as the relationship between multiplication and division (e.g.,
knowing that 8 × 5 = 40, one knows 40 ÷ 5 = 8) or properties of operations. By the end of Grade 3, know from memory all products
of two one-digit numbers.
Solve problems involving the four operations, and identify and explain patterns in arithmetic.
3.OA.8 Solve two-step word problems using the four operations. Represent these problems using equations with a letter standing for
the unknown quantity. Assess the reasonableness of answers using mental computation and estimation strategies including
rounding. (This standard is limited to problems posed with whole numbers and having whole number answers; students should
know how to perform operations in the conventional order when there are no parentheses to specify a particular order (Order of
Operations).
3.OA.9 Identify arithmetic patterns (including patterns in the addition table or multiplication table), and explain them using properties
of operations. For example, observe that 4 times a number is always even, and explain why 4 times a number can be decomposed
into two equal addends.
3.NBT.3 Multiply one-digit whole numbers by multiples of 10 in the range 10-90 (place value, properties of operations)
SMP: Student Math Practices Overarching habits of mind of a productive mathematical thinker:
MP1 Make sense of problems and persevere in solving
MP6 Attend to precision.
The following do not necessarily represent all practices that might be evident, but are high leverage practices to be emphasized
during this unit:
MP2 Reason abstractly and quantitatively
MP8 Look for and express regularity in repeated reasoning.
Connections Across Math
Connections Across Content
Career & College Readiness Anchor Standards: Language Arts
Connecting Math Standards for depth and practice.
Use charts, graphs and measurement contexts for problemsolving opportunities. These extended connections can help
students think strategically as they work with multiple contexts
to solve problems. This also provides foundations for this
content as is comes up later in the year.
3.MD.2, 3, 7
Curriculum, Instruction, & Assessment
RF As students read mathematical contexts, they will draw upon
foundational skills to recognize features of story problems,
recognize and understand various conventions and symbols of
mathematics; Identify and know common prefixes, derivational
suffixes, common Latin prefixes, suffixes; read grade-level text
with purpose and understanding.
RL1 & RI1 Ask and answer questions to demonstrate
understanding of a text, referring explicitly to the text as the
basis for answers.
W10 Write routinely over extended and shorter time frames for a
range of discipline-specific tasks, purposes, and audiences.
SL Engage effectively in a range of collaborative discussions with
diverse partners on topics and texts, building on others’ ideas
and expressing their own clearly.
b) …listening to others with care, speak on topic
c) Ask questions to check understanding…
d) Explain their own ideas and understanding…
Rev. May 3, 2013
Salem-Keizer Public Schools
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Unit 1: Foundations of Multiplication & Division
DRAFT
Building Academic Language
Strategies embedded provide examples within context of this unit and is not an exhaustive list. Teachers customize lessons and
strategies throughout instruction to benefit student learning and language development. Instructional Scaffolds for Levels of
English Proficiency for comprehensive listing of scaffolds for levels of EP.
What Students Can Do
General descriptions representing levels
of English Proficiency.
Beginning
• Gestures to communicate basic needs
• Use high frequency words/basic phrases
• Produce words/phrases/simple sentences w/
common nouns & verbs
Early Intermediate
• Use past tense of common verbs
• Dramatic increases in comprehension of
general meaning
• Grasp some specific meaning
Intermediate
• With supports such as signal words/phrases,
sentence and paragraph frames, can express
ideas, describe events, give information orally
and in writing
• Learn to use more precise vocabulary
(synonyms, antonyms, basic idioms)
• Comprehend/discuss main ideas and basic
concepts
• Write basic information expanded responses
• Comprehension of general meaning/some
specific meaning
• Can read familiar below grade-level text
independently
• Can read grade-level text with scaffolds
• Language focus on pronoun usage, past
tense verb markers
Advanced
• Comprehend general and implied meaning,
including idiomatic and figurative language
• Initiate and negotiate communication using
complex sentence structures and vocabulary
• Demonstrate mastery of language
conventions for both formal and informal use
What Students Need to be
Taught & Accomplish
• Respond by pointing, circling,
gesturing, manipulating objects/pictures
• Use words/phrase to tell, ask, answer (yes/no)
questions about who, what, where
• Read high frequency words
• Draw, label, match, construct simple
sentences using frames/word banks
Bridges Work Place Sentence Frames
• Recite familiar songs/poems
Chants, poems, songs focused on
multiplication/division:
Have Fun Teaching Home Page (YouTube)
Counting Song Videos Home Page
Count by 2
Count by 3
Count by 4
Count by 5
Count by 6
Count by 7
Count by 8
Count by 9
Count by 10
• Make presentations, identify main
idea/supporting details/key concepts,
hypothesize, infer word meaning from context
and affixes Students present, explain and
justify solutions in pairs, small groups on
regular basis to check for understanding,
offer feedback, develop speaking and
listening skills.
• Debate/support point of view, persuade,
justify Students present, explain and justify
solutions independently, teacher provides
feedback to revisit work. Students are then
given opportunity to present formal work
to class
Effective Instructional
Practices
• Abundant exposure to basic vocabulary
supported by visuals and realia (real objects):
E.g., Connecting cubes, base ten pieces,
number lines, hundreds grids and charts,
visual dictionary
Maths Dictionary for kids
Pictures of things in Groups - SmartFile
• Make explicit connections to known
vocabulary and concepts
• Model simple sentence patterns with
vocabulary to support language production
Academic Language Support Math Focus
Making Meaning: Compare and Contrast
Bridges Work Place Sentence Frames
• Repetition to internalize new vocabulary and
language structures
Grade level vocabulary
cards
ENG SP List
Classroom Activities to build , use, practice
academic language. These opportunities
provide scaffolds for using targeted
academic language with content to build
language skills and content knowledge.
Multi-Language Dictionary
SBAC Glossary
Virtual Library of Math Literature
Discourse Protocols to build routines for
regular mathematical discourse (student-tostudent) to provide feedback to students.
Explore word relationships with word sort and
graphic organizers
• Develop authentic practice opportunities for
fluency and automaticity in communication.
These opportunities are embedded
throughout work shop activities. Teachers
make these explicit for students to meet
language needs.
Curriculum, Instruction, & Assessment
Rev. May 3, 2013
Salem-Keizer Public Schools
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Unit 1: Foundations of Multiplication & Division
DRAFT
Foundational Lessons to Get Started Lessons use current adopted materials to begin teaching
standards. Teachers customize instruction and plan next steps based on data from formative assessment.
Inv1 Foundation Lessons click on link
Inv2 Foundation Lessons click on link
NEW Inv2 CC U5 Lessons
NEW Inv2 CC U5 Lessons
file contains teacher
pages and Eng/Sp pages. Student pages for foundation
lessons are included in files below.
Lessons work with multiples of 11 and 12. This is a natural
extension, but standards focus on multiples of single-digit
factors. Adjust lessons as necessary to fit your class.
file contains teacher
pages and Eng/Sp pages. Student pages for foundation lessons
are included in files below.
Lessons work with multiples of 11 and 12. This is a natural
extension, but standards focus on multiples of single-digit
factors. Adjust lessons as necessary to fit your class.
STUDENT PRINT pdf files for Foundational Lessons are prepared and ready to send to Repro/DSF.
NC and Workshop
are teacher-selected components and are NOT included in these print files.
Student Activity Books must be purchased each year. There
are no black line masters and printing copies of the books
Lessons: Eng Sp
would be in violation of copyright laws.
Skip Counting books Eng & Sp are the same
Array Cards (print on cardstock): Eng & Sp are same
Exit Tickets: Eng
Sp
ANSWER KEY/Rubric
Student print (outside of Student Activity Books) PDF files
matching Foundational Lessons
Lessons: Eng Sp
Skip Counting books Eng & Sp are the same
Array Cards (print on cardstock): Eng & Sp are same
Exit Tickets: Eng Sp
Workshop Resources Standards-based resources for the “Explore” segment of lesson (could be whole group,
guided groups for intervention/enrichment). Pdf files for lessons and student print (ENG, SP) are linked below.
3.OA.1, 3
Multiplication
Problems
3.OA.1,2,3
Multiplication
Challenge
Eng-Sp (print ½
class set)
3.OA.1,3
Each Orange Has 8
Slices
Literature-based
(no print)
3.OA.1,3,4,9
Product Bingo
3.OA.1,3
Array Picture Cards
3.OA.4
Missing Numbers
3.NBT.3
Multiples of Ten
Multiply
3.OA.5
Decompose a Factor
3.OA.2,3,7
Sharing or Grouping
3.OA.9
Patterns in the
Multiplication Table
Eng Sp
3.OA.7
Concentration
Technology-based
3.OA.1,3
Six Sid Dinner
Literature-based
3.OA.1,3
Amanda Bean’s
Amazing Dream
Literature-based
(no print)
(no print)
What’s Missing Bingo
3.OA.4
3.OA.5
Split a Factor
3.OA.9
Two Step Number
Patterns
3.OA.3,7
Array Challenge
3.OA.3,7
Spinning for Arrays
3.OA.4,6
Division as Unknown
Factor Problems
3.OA.3,7
Building Arrays
3.OA.7
Spinning Around
Multiplication
3.OA.8
Two-Step Word
Problems
3.OA.9
Drawing
Multiplication
Patterns
3.OA.9
Using Number
Patterns to Describe
Multiples
3.OA.9
Odd, Even Products
3.OA.9
Increasing and
Decreasing Number
Patterns
Eng-Sp (print ½
class set)
Multiplication Games for work shop or home
Cookie Caper
Multiplication Table
Camel Tables
Wades Workout
Games use models and vocabulary for
practice after classroom instruction
Whole Group Resources
Tool: Visualize Arrays
ThinkingBlocks Multiplication/Division Models
Array Back Then Video: Understanding Multiplication. Discovery Learning (available through Library Media)
Curriculum, Instruction, & Assessment
Rev. May 3, 2013
Salem-Keizer Public Schools
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Unit 1: Foundations of Multiplication & Division
DRAFT
Instructional Resources
Targeted for this Unit of Study
General Resources
Illuminations - NCTM Searchable by domain, grade
SMART Notebooks:
Illustrative Mathematics Searchable by standard.
Student created Mult/Div problems Set A Set B
NRICH Extensive work shop & problem-solving resources,
All About Multiplication 4 sessions, Illuminations
K-5 Instructional Resources Listing by CCSSM, Grade
Level
3OA9 Patterns Mult Table
GLAD chants for math
CCSSM Tasks Listing by standard
Bridges CC Supplements:
DATA SETS & GRAPHS: varied types of graphs, charts, data
A1 Equal Expressions Eng Sp
A2 Basic Multiplication & Division Eng Sp
A7 Multiplication Beyond the Basic Facts Eng Sp
for use in creating instructional opportunities, student
assessments
Workshop Student Planner blank
Rubric to evaluate CCSSM lessons and units of study .
ODE uses similar rubric to evaluate materials for
adoption at state level.
Bridges Home Connections 3-HC
Bridges Practice Book/Pages Eng Sp KEY
nd
Gr3: Inv 2
Correlation CCSSM
Math Learning Center Gr3 NC Planning Gr3
Bridges/MLC: Correlation to CCSSM
Family Support (Home Connections, games, e.g.) Gr3
Inv2 Grade 3 CCSSM support: 3-CC Planner: U1
U3 U4 U5 U6 U7 U8 U9
U2
Pearson Online Games & Activities Grade 2-3
Assessment Options Assessments are available in both Spanish and English
Proficiency Rubrics:
CCSSM Tasks (U:Drive) K-5 Task List
Rubric for scoring Math Practices
3OA8, 3MD3, 3.MD.7abc Class Play
3OA7, 3MD3 Chips & Sodas
3OA7, 3MD3 Donut Party
3OA8, 3MD3 Bird Survey
_______________________________________
Formative options:
• Pre/post
• Exit tickets
• Other assessments embedded in Investigations materials
Illustrative Mathematics Tasks:
3OA3 Analyzing Word Problems; Gifts from Grandma;
Two Interpretations of Division
Summative options;
• must be multiple pieces of evidence to support
• no one assessment should be used to report overall progress
3OA8 Stamp Collection
3OA9 Addition Patterns Making a Ten Symmetry
Addition Table
.
Work Sample Resources Performance tasks help prepare students on their path to being Career and
College ready through application of their learning, connected to real world problem solving. Work samples can be a
problem embedded in the work students are already doing, performed independently by students. Work is scored with the ODE Math
scoring guide. Students can revise their work after initial scoring using feedback form. For re-scoring, the work must continue to be
un-coached, independent work.
TASKS:
ODE Math Scoring Guide ENG SP Used at grade 3-5. Use at earlier grades: PLCs may want to modify rubric based on
grade level and task expectations with standards.
Student Feedback form This can be used to facilitate better understanding of scoring student work. It is recommended that
students are shown examples of strong and weak work matched to the scoring guide.
Lesson: Helping Students Understand & Use Scoring Guides Customize to fit your target audience
Curriculum, Instruction, & Assessment
Rev. May 3, 2013
Salem-Keizer Public Schools
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Unit 1: Foundations of Multiplication & Division
DRAFT
Professional Development Support for CCSSM
PD 360: Common Core 360
Look for “In The Classroom” to view videos of
standards being implemented. Look for
PROGRESSIONS: Target a particular standard and
you will be able to view learning that comes prior to
and following targeted content.
___________________________
Teacher Rubric: Fostering Student Math Practices in the
Classroom
Inside Mathematics Professional resource for educators wishing to
improve student s’ mathematical learning and understanding.
Illustrative Mathematics for Progressions Select grade,
then look for “Illustrations” to view tasks.
3.OA.7 Defining fluency, and strategies to build
conceptual understanding and fluency (2 parts)
3.OA.9 Identifying, explaining patterns.
Teacher Reflection
What worked well?
What did I modify?
What should I watch for?
Curriculum, Instruction, & Assessment
Rev. May 3, 2013
Salem-Keizer Public Schools
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